The correct answer is D. Only sentence D uses "mission" as a direct object.
By rewriting this question and changing the order a bit, it will become clear that "mission" is a direct object.
Consider: Sally Ride did fly which mission for NASA? The meaning of the sentence is the same as the original, but now we have put the parts of the sentence in an order that will help us identify the parts. Now we can easily see that the subject of the sentence is "Sally Ride." The verb of the sentence is "did fly." Finally, "mission" is the direct object.
In sentence A, "mission" is the subject of the sentence; in sentence B, "mission" is the object of the preposition "on"; and in sentence C, "mission" is also the object of the preposition "during."
Only in sentence D is "mission" a direct object.